Question

Look again at Figure 11.17 (p. 438). Suppose that the marginal costs c1 and c2 were zero. Show that in this case, pure bundling, not mixed bundling, is the most profitable pricing strategy. What price should be charged for the bundle? What will the firm’s profit be?

Short answer

The pure bundling pricing policy will provide the producer more profits than the mixed bundling pricing policy. The bundle should be priced at $100. The firm’s profit would be $400.

Step-by-step solution

Step 1. Compare the profits from pure bundling and mixed bundling

• Profit under pure bundling:Under the pure bundling pricing strategy, the producer will sell a package of two goods to the consumers. It will charge a price equal to the maximum reservation price that the customer is willing to pay for the combination of both the goods. Since marginal cost is zero for both the goods, profit will be equal to the price of goods.

The producer will sell both the goods as a single package at a maximum price of $100. The diagram suggests each consumer can offer a reservation price of $100 for the package of both the goods. The producer will sell four packages and earn a total profit of $400.

• Profit under mixed bundling:Under the mixed bundling pricing policy, the producer tries to earn maximum profit by applying a separate pricing policy for some consumers and a pure bundling pricing policy for others. The total profit will be the sum of profits earned from all the consumers.

Suppose the producer applies a mixed bundling policy for the consumers shown in the figure. In that case, it will earn maximum by applying a separate pricing policy for consumers A and D and bundling pricing policy for consumers B and C. Thus. The producer will charge $90 for Good 2 from Consumer A, $90 for Good 1 from Consumer D, and a bundling price of $100 for both the goods from Consumer B and Consumer C.

The total profit earned by the producer will be the sum of prices charged from each consumer. Thus, the total profit will be $380 (90+90+100+100).

Comparing both the pricing strategies, the pure bundling pricing policy provides more profit to the producer. Hence, the pure bundling pricing policy provides more profits to the producer in the absence of any marginal costs.

Step 2. Determination of prices for the bundle

It is evident that a pure bundling pricing policy will be ideal for the producer because this pricing policy provides maximum profit compared to other pricing policies. Under this policy, the producer will charge a price equal to of maximum reservation price that the consumers are willing to pay for the bundle. Since all the four consumers are willing to pay $100 for the bundle (combination of both the goods), the producer charge $100 for the bundle. Therefore, the price of the bundle would be $100.

Step 3. Determining the firm’s profit

Since the marginal cost of the goods is zero, the firm’s profit from each good would be the price of that good. Hence, the firm's total profit would be the sum of the price paid by Consumer A, Consumer B, Consumer C, and Consumer D for a unit of the bundle.

Since each consumer has paid the same price for the bundle, the firm's total profit would be 4×100 = $400.